论文标题
使用近似零偏置耦合的浓度不平等，并应用于Hoeffding的Ewens分布下的统计数据
Concentration inequalities using approximate zero bias couplings with applications to Hoeffding's statistic under the Ewens distribution
论文作者
论文摘要
我们证明，对于随机变量$ y $，$ p（y \ ge t）\ le \ exp（-b（t））$的集中不平等，使用Stein方法中的耦合技术，该方法均为零和方差$σ^2 $，该方法是所谓的Zero Zero kias couplings of stein方法。还显示了随机排列具有带有参数$θ> 0 $的ewens分布的应用程序的应用程序。然后提供了一些模拟实验，以可视化Hoeffding统计量和我们的边界的尾巴概率。基于模拟结果，我们的界限效果很好，尤其是当$θ\ le 1 $时。
We prove concentration inequalities of the form $P(Y \ge t) \le \exp(-B(t))$ for a random variable $Y$ with mean zero and variance $σ^2$ using a coupling technique from Stein's method that is so-called approximate zero bias couplings. Applications to the Hoeffding's statistic where the random permutation has the Ewens distribution with parameter $θ>0$ are also presented. A few simulation experiments are then provided to visualize the tail probability of the Hoeffding's statistic and our bounds. Based on the simulation results, our bounds work well especially when $θ\le 1$.
